Introduction to Applied Statistics

Course Description

This course will provide students with a practical introduction to the highlights of descriptive and inferential statistics, including data production and some basic probability. A major goal of this course will be to make students statistically literate, i.e. able to determine the validity of statistical information available in the media and literature. This course will make extensive use of technology, enabling the focus to be more on interpreting statistics rather than doing computations. The course will also include writing assignments designed to teach the students how to present technical information in a clear and concise manner.

Course Big Ideas

Different variables are summarized in different ways.
There are both good and bad ways to collect data.
Random events have predictable results.
What can be inferred from the data we collected.

Course Essential Questions

What is the best way (graphically and numerically) to summarize this data?
How can I make sure my data is random?
What conclusion can be drawn from this study?
How well does this one sample represent a population?
What is the appropriate inference procedure to use?

Course Competencies

Use the appropriate graphical and numerical summaries for quantitative and categorical data.
Understand which summary statistics are the most useful.
Our data is only as good as the method we collected it.
Observational studies allow us to generalize results, but experiments allow us to draw a cause and effect conclusion.
Probability allows me to make random events have predictable results.
There are 4 basic inference procedures, and they allow me to draw conclusions to a larger population based on a single sample.

Course Assessments

Unit quizzes
Unit tests
Informal and formal writing assignments
Presentations
Informal check of daily assignments

Course Units

Unit 1: Exploring Data

Standards

AP College Board Statistics CED Skills

DA.2.A Describe data presented numerically or graphically.
DA.2.B Construct numerical or graphical representations of distributions.
DA.2.C Calculate summary statistics, relative positions of points within a distribution, correlation, and predicted response.
DA.2.D Compare distributions or relative positions of points within a distribution.
PS.3.A Determine relative frequencies, proportions, or probabilities using simulation or calculations.
SA.4.B Interpret statistical calculations and findings to assign meaning or assess a claim.

Know

Categorical variables represent names or labels.
Quantitative variables take on a numerical value.
When to use a bar chart, histogram, stem plot, box plot, to summarize data.
When to use mean, median, interquartile range, standard deviation to summarize data.
What outliers are and how they affect graphs and summary statistics.
Define the parameters of a normal distribution such as shape, center and spread.
The 68%, 95%, 99.7% empirical rule.
How to find z-scores.
When to use side-by-side, segmented or mosaic bar graphs.
How to use two-way tables, marginal and conditional frequencies.
Describe a scatter plot and its explanatory and response variables.
What the correlation of a scatter plot is and what it tells us.
Find the least squares regression line and use it for predictions.

Understanding/Key Learning

Do

Determine if a variable is categorical or quantitative.
Create the appropriate graphical displays for data.
Calculate the appropriate numerical summaries of data.
Analyze both graphical and numerical summaries of data to draw a conclusion.
Defend a conclusion based on summaries statistics.
Calculate z-scores and outliers.
Support a claim that a normal distribution is the appropriate model for data.
Compare two categorical variables for the same group of subjects.
Describe the strength and direction between two quantitative variables.
Determine the linear regression equation and use it to make predictions.

Unit Essential Questions

Lesson Essential Questions

How do I describe the relationship between two categorical variables?
What value is the “typical” value in a data set?
How do I describe the distribution of a quantitative variable?
How do I measure the position of a data value in the data set?
What types of variables exist?
How do outliers affect the graph?
How do outliers affect the measures of central tendency and spread?
How do I describe the association between two quantitative variables?
How do I make predictions about one quantitative variable from another quantitative variable?
How good are the predictions we make?
What is a normal distribution?

Materials/Resources

Vocabulary

Data
Variability
Categorical/Quantitative Variables
Observational Unit
Distribution
Bar Graph
Dotplot
Two way table
Marginal Distribution
Conditional Distribution
Relative Risk
Mean
Median
Standard Deviation
Range
Scatter Plot
Least squares
Line of regression
Strength, Direction, form
Correlation Coefficient
Statistical Tendency
Normal Distribution
Interquartile Range (IQR)
Box Plots
Stem Plot
Outliers
Z-Score

A population consists of all items or subjects of interest, but a sample is just a subset.
The characteristics of an observational study and what conclusions can be drawn.
The characteristics of an experiment and what conclusions can be drawn.
What makes a sample a random sample.
The different types of random sampling such as simple, stratified, and cluster.
The sampling methods that lead to bias results such as voluntary, undercoverage, and nonresponse.
The components of an experiment such as explanatory, response, confounding variables, randomness, blind, and placebo effect.

Understanding/Key Learning

Do

Determine if data comes from a population or sample.
Explain if the explanatory variable was assigned to subjects or chosen by subjects.
Identify explanatory and response variables.
Describe how to collect data from a simple random sample.
Categorize the type of random sampling done in an observational study.
Argue why results are biased.
Describe how to randomly assign a treatment to subjects.
Defend a cause and effect conclusion from an experiment.

DA.2.B Construct numerical or graphical representations of distributions.
PS.3.A Determine relative frequencies, proportions, or probabilities using simulation or calculations.
PS.3.B Determine parameters for probability distributions.
PS.3.C Describe probability distributions.
SA.4.B Interpret statistical calculations and findings to assign meaning or assess a claim.

Know

A random process produces outcomes determined by chance, and events are collections of outcomes.
The law of large numbers and how the results tend to converge toward the true probability.
How to find a sample space and use it to find probability.
The probability of an event is a number between 0 and 1, inclusive.
What mutually exclusive events are.
Calculate conditional probability and the multiplication rules for probability.
How to show events are independent.
The values of a random variable are the numerical outcomes of random behavior.
The results from random variables can be summarized both numerically and graphically in a similar way as data.
Parameters for binomial random variables such as shape, center, spread.
The Central Limit Theorem and how it helps us create normal distributions.

Understanding/Key Learning

Do

Describe the sample space for an event.
Determine the number of outcomes in favor.
Design a simulation to find outcomes of a random process.
Prove that two events are mutually exclusive.
Prove that two events are independent.
Combine the probability from multiple events.
Display the results of a binomial random variable both numerically and graphically.
Calculate probabilities using the general addition rule, multiplication rule, and conditional probability formula.
Argue that a distribution is normal using the conditions of the Central Limit Theorem.
Support a decision based on the expected probability.

SSM.1.D Identify an appropriate inference method for confidence intervals.
SSM.1.E Identify an appropriate inference method for significance tests.
SSM.1.F Identify null and alternative hypotheses.
PS.3.D Construct a confidence interval, provided conditions for inference are met.
PS.3.E Calculate a test statistic and find a p-value, provided conditions for inference are met.
SA.4.A Make an appropriate claim or draw an appropriate conclusion.

Know

The procedures for a one sample z-interval for proportions.
The procedures for a one sample t-interval for means.
How to find standard error and margin of error.
The true parameter can be anywhere in the interval.
The difference between a null and alternative hypothesis.
The procedures for a one sample z-test for proportions.
The procedures for a one sample t-test for means.
If a p-value is large or small.

Understanding/Key Learning

Do

Recognize if the conditions for a confidence interval have been met.
Recognize if the conditions for a significance test have been met.
Dissect the different parts of a confidence interval such as estimator, standard error, margin of error.
Explain how changing one of these parts will affect the interval.
Interpret a confidence interval to generalize results to a larger population.
Determine a null and alternative hypothesis.
Compare a p-value to an alpha value.
Make a claim about a hypothesis based on the results of a significance test.
Draw the appropriate conclusion based on the p-value.